On existence of Mersenne and Hadamard matrices

There have been considered conditions of existence of Mersenne matrices. Analyzing conditions of existence of Belevitch matrices it has been shown that restrictions characteristic for integer matrices do not influence on matrices with rational and irrational values of elements to which Mersenne matrices belong. There has been given a dependency of elements values of an order of Mersenne matrices, the absence of critical points in the graph of this dependency has been shown. There has been commented a connection of conjectures of existence of Hadamard and Mersenne matrices.